if the height of a regular triangular pyramid base equals 57.3, the base equals 6, and the slant height equals 8. What is the surface area?
The formula to calculate the surface area of a regular triangular pyramid is given by:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
In this case, the base of the triangular pyramid is an equilateral triangle since it is a regular pyramid. Therefore, the perimeter of the base is 3 * base length.
Given:
Height of triangular pyramid base = 57.3
Base length = 6
Slant height = 8
To calculate the surface area, we can use the formula mentioned above.
Base Area = (sqrt(3) / 4) * (base length)^2
= (sqrt(3) / 4) * 6^2
= (sqrt(3) / 4) * 36
= 9sqrt(3)
Perimeter of base = 3 * base length
= 3 * 6
= 18
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
= 9sqrt(3) + (1/2) * 18 * 8
= 9sqrt(3) + 144
≈ 162.535
Therefore, the surface area of the triangular pyramid is approximately 162.535 square units.